MinT - Information on Result #547973

Information on Result #547973

There is no linear OA(7³¹, 53, F₇, 27) (dual of [53, 22, 28]-code), because constructionÂ Y1 would yield

OA(7³⁰, 34, S₇, 27), but
- the linear programming bound shows that MÂ â‰¥ 2186 316008 197149 034522 735153 / 88 > 7³⁰ [i]
linear OA(7²², 53, F₇, 19) (dual of [53, 31, 20]-code), but
- discarding factors / shortening the dual code would yield linear OA(7²², 46, F₇, 19) (dual of [46, 24, 20]-code), but
  - constructionÂ Y1 [i] would yield
    1. OA(7²¹, 25, S₇, 19), but
      - the linear programming bound shows that MÂ â‰¥ 105 565168 311740 677323 / 184 > 7²¹ [i]
    2. linear OA(7²⁴, 46, F₇, 21) (dual of [46, 22, 22]-code), but
      - discarding factors / shortening the dual code would yield linear OA(7²⁴, 31, F₇, 21) (dual of [31, 7, 22]-code), but
        residual code [i] would yield OA(7³, 9, S₇, 3), but
        bound for OAs with index unity [i]

Mode: Bound (linear).

None.

None.